What is the integral of (x-2)/(sqrt(x+1)) ?

The integral of (x-2)/(sqrt(x+1)) is 2(x-2)sqrt(x+1)-4/3 (x+1)^{3/2}+C

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integral of (x-2)/(sqrt(x+1))

\int \frac{x - 2}{x + 1} d x

2 (x - 2) x + 1 - \frac{4}{3} (x + 1)^{\frac{3}{2}} + C

Solution steps

\int \frac{x - 2}{x + 1} d x

Apply Integration By Parts

= 2 (x - 2) x + 1 - \int 2 x + 1 d x

\int 2 x + 1 d x = \frac{4}{3} (x + 1)^{\frac{3}{2}}

= 2 (x - 2) x + 1 - \frac{4}{3} (x + 1)^{\frac{3}{2}}

Add a constant to the solution

= 2 (x - 2) x + 1 - \frac{4}{3} (x + 1)^{\frac{3}{2}} + C

What is the integral of (x-2)/(sqrt(x+1)) ?
The integral of (x-2)/(sqrt(x+1)) is 2(x-2)sqrt(x+1)-4/3 (x+1)^{3/2}+C